The present invention relates generally to the field of imaging systems. In particular, the invention relates to a system and method for reconstructing useful images from cone beam tomographic projections with missing data.
CT scanners operate by projecting fan shaped or cone shaped X-ray beams through an object. The X-ray beams are generated by an X-ray source, and are generally collimated prior to passing through the object being scanned. The attenuated beams are then detected by a set of detector elements. The detector element produces a signal based on the intensity of the attenuated X-ray beams, and the signals are processed to produce projections. By using reconstruction techniques, such as filtered backprojection, useful images are formed from these projections.
A computer is able to process and reconstruct images of the portions of the object responsible for the radiation attenuation. As will be appreciated by those skilled in the art, these images are computed by processing a series of angularly displaced projection images. This data is then reconstructed to produce the reconstructed image, which is typically displayed on a cathode ray tube, and may be printed or reproduced on film.
Direct reconstruction techniques, such as filtered backprojection, are generally fast and computationally efficient, since they allow reconstruction of a three-dimensional image data set in a single reconstruction step. Unfortunately, direct reconstruction techniques require that data be available on a regular grid of detector elements, conforming to some mathematically defined surface or volume. Furthermore, for proper operation of these direct reconstruction techniques, all of the detectors must be present and functional. In practice, as will be appreciated by those skilled in the art, CT systems may possess defective, missing, non-functional detector elements or gaps in-between detector elements. As a result, a number of CT projection data measurements may be missing and this in turn causes the projection data measurements to be unavailable on a regular set of coordinates. Therefore, direct reconstruction techniques cannot be directly applied to data from such CT systems.
A number of alternative techniques have been proposed to address the subject of missing projection data measurements. Some of these techniques include using a predefined value for the missing data, interpolating the missing values from available neighboring values, or using “complementary rays” obtained from other parts of an image scan. As will be appreciated by those skilled in the art, using a predefined value for the missing data results generally leads to severe artifacts and interpolation is possible only if the missing data regions are sufficiently small. Furthermore, the “complementary rays” technique works well in two-dimensional space, while its corresponding behavior in three-dimensional space is unsatisfactory.
Another technique that has been proposed to address the subject of missing data measurements is to perform an iterative reconstruction of the volume to be imaged. As will be appreciated by those skilled in the art, iterative reconstruction techniques improve image quality through an iterative step. In general, iterative reconstruction techniques start with an initial guess of the reconstruction volume, and then sequentially refine that guess by comparing data synthesized from this estimated volume with the actual measurements. Discrepancies between the synthesized and measured data are used to correct the estimated volume. This process continues until some threshold criteria are met. However, iterative reconstruction techniques require enormous amounts of computation and are not useful in practice unless the image volume to be reconstructed is small. Furthermore, iterative reconstruction techniques are much slower than direct reconstruction techniques requiring 10-100 times the computational cost as compared to direct reconstruction techniques.
Unlike direct reconstruction techniques, iterative reconstruction techniques can effectively handle missing projection data measurements since they do not require that all the projection data measurements be available on regular sets of co-ordinates. Therefore, there is a need for a technique that combines the flexibility provided by iterative reconstruction techniques with the speed of a direct reconstruction technique for reconstructing cone beam tomographic projections that comprise missing data measurements.